jessecmckeown

alexyar:

jessecmckeown:

alexyar:

shadowpeoplearejerks:

reddragdiva:

alexyar:

No, google, when I search for “rational homotopy theory” I really don’t want to search in RationalWiki

uh

when even i goggle for “rational homotopy theory” (with or without quotes) i don’t get rationalwiki in the first five pages

so thanks for (it seems) reading rationalwiki more than i do

your filter bubble loves you and knows more about you than you do yourself

Nothing useful is in the first five pages :(

Try just looking for “Sullivan minimal model” instead?

lol sure, i know how to use google, i was looking for a particular paper and “rational homotopy theory” was part of the title

it wasn’t your gügle skills I was worried about

Source: alexyar

Comments

alexyar:

shadowpeoplearejerks:

reddragdiva:

alexyar:

No, google, when I search for “rational homotopy theory” I really don’t want to search in RationalWiki

uh

when even i goggle for “rational homotopy theory” (with or without quotes) i don’t get rationalwiki in the first five pages

so thanks for (it seems) reading rationalwiki more than i do

your filter bubble loves you and knows more about you than you do yourself

Nothing useful is in the first five pages :(

Try just looking for “Sullivan minimal model” instead?

Source: alexyar

Comments

A little thing about MU

It’s very easy to be cagey about what really is the fibering $E\to \deloop U_k$ with two sections whose mapping cone $E/{\deloop U_k}$ is the Thom space $MU(k)$; but it’s also easy to be explicit.

The fiber of $E$ is the (unreduced!) suspension of the natural action of $U_k$ on $\sph^{2k-1}$ (the unit vectors in $\mathbb{C}^{k}$); which is to say the natural action of $U_k$ on the homogeneous space $U_k/U_{k-1}$ … or, prefering to avoid overloading “$/$”, $\sph^{2k-1}$ is the fiber of $\deloop U_{k-1} \to \deloop U_k$.

So: Ah! The total space $E$ we want is the self-pushout $$\begin{CD} \deloop U_{k-1} @>\deloop j > > \deloop U_k \\ @V\deloop j VV @VV N V \\ \deloop U_k @> > S > E \end{CD} $$ which means that $MU(k) = \Th(\deloop U_k , \tau \sph^{2k}) \simeq \deloop U_k / \deloop U_{k-1} $.

And that doesn’t get mentioned enough, I don’t think.

Comments

altier:

alexyar:

oh for god’s sake

a brief version: it’s not “Rolle’s theorem is just the MVT”, it’s “the MVT is just Rolle’s theorem”

Right, aren’t the proofs nearly identical?

Exercise: State and Prove the Mean Value Theorem.

Source: alexyar

Comments

Amateur-tip

The function “render” in the gimp extension “mathmap” allows in-place tail-recursion. In certain circumstances, this can save you a lot of time. E.g.,

filter repatch ( image in , float size : 0-1 (.7) )
    tmp = rgba:[0,0,0,0];
    for z = 0 .. 5 do
	ctrcolor = toRGBA(hsva:[ a/(2*pi) , 1 , 1 , 1]);
	termcolor = in((xy - toXY(ra:[size,z*pi/3]))*3 );
	tmp = tmp + ctrcolor * .5 * termcolor[4] + termcolor * .5
    end;
    tmp + in( toXY( ra + ra:[0,5*pi/6]) * sqrt(3)) * .5
end

filter tail_ifs ( image in , float size : 0-1 (.7) , int depth : 0-12 (2))
    if depth == 0 then
      in(xy)
    else
      hold = render (tail_ifs(in,size,depth-1)) ;
      repatch (hold,size,xy)
    end
end

Writing tail_ifs(...) instead of hold will parse, BUT it seems that this will effectively lead to seven-fold branching in each recursive call to tail_ifs via the “in” argument to repatch.
PS. … can you tell that I’m being frustrated by unrelated things?

Comments

both the above links have the property that any four of the rings include two copies of the Borromean three-loop link; in one, the Borromean sublinks are adjacent in the convex-pentagon cyclic order, in the other these sublinks are in star-pentagram cyclic order.
Silly Question: are these links secretly isotopic?

Comments

I was in a mood for noodling with the GIMP

Comments